Related papers: Patterns theory and geodesic automatic structure f…

In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent…

Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a…

Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. The…

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…

It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…

This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…

In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex semisimple Lie groups and to spherical Hecke rings…

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…

Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product…

We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present…

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…

Let M be a manifold, and G a Lie group which satisfies the unique extension property. An (M,G) manifold N is a manifold endowed with an atlas (U_i,f_i) where f_i is a diffeomorphism between U_i and an open set of M such that the coordinates…

We describe the development of the theory of automatic groups. We begin with a historical introduction, define the concepts of automatic, biautomatic and combable groups, derive basic properties, then explain how hyperbolic groups and the…

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We…

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future…